Why did the British rule Palestine in the Arab-Israeli War of 1948?

The British did not rule Palestine during the Arab-Israeli War of 1948-9, leaving just before the war began. It was actually the British withdrawal from Mandatory Palestine that allowed Israel to declare independence. This declaration, in turn, was what precipitated the Arab invasion of the former British Mandate of Palestine and of Israel specifically.

As for why the British were ruling Mandatory Palestine from 1919-1948, this was as a result of the Treaty of Versailles which gave numerous former Ottoman Territories to Great Britain and France to supervise as they organized properly for their future independence.